Questions on Algebra: Sequences of numbers, series and how to sum them answered by real tutors!

Tutors Answer Your Questions about Sequences-and-series (FREE)

Question 27288: Use the formula for an arithmetic series to find each sum.
40+42+44+...+68.
Thank you very much
Click here to see answer by sdmmadam@yahoo.com(530)

Question 26650: 1) Identify the fifth term in the sequence in which a^2=40 and r=1/2
2) Find the sum of the geometric series in which a^1=125,r=2/5, and n=4
Click here to see answer by venugopalramana(3286)

Question 27325: what number less than 3000 when divided by 10 has a remainder of 9 and when divided by 9 has a remainder of 8 and when divided by 8 has a remainder of 7 and when divided by 7 has a remiander of 6 and when divided by 6 has a remainder of 5 and when divided by 5 has a remainder of 4 when divided by 4 has a reaminder of 3 when divided by 3 has a remainder of 2 and when divided by 2 has a remainder of 1 and when divided by has a remainder of 0
Click here to see answer by venugopalramana(3286)

Question 28030: find the mean, median, and mode of the set: 1,2,2,3,3,3,4,4,4,4
Click here to see answer by venugopalramana(3286)

Question 29695: 3) Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following.
b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms?

c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms?

d) What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?

Click here to see answer by sdmmadam@yahoo.com(530)

Question 29783: 1)Use the arithmetic sequence of numbers 2, 4, 6, 8, 10… to find the following:
a)What is d, the difference between any 2 terms?
Answer:
Show work in this space.

b)Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer:
Show work in this space.

c)Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Answer:
Show work in this space.

d)Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?
Answer:
Show work in this space.

e)What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)?
Answer:
Click here to see answer by venugopalramana(3286)

Question 29589: I am having trouble with this problem, could you please help me.
3) Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following.

PROBLEMS:
b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms?

c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms?

d) What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?
Thank you in advance for all your help.
Click here to see answer by sdmmadam@yahoo.com(530)

Question 30045: The value of square-root(2/pi) * Integral(e to the power -square(t)/2 ),
where "t" is a variable from 4 to infinity is equal to what?
Click here to see answer by AnlytcPhil(1278)

Question 30508: I'm looking to find th 52nd term of the following harmonic series.
1+ 1/5 + 1/9 + 1/13 + 1/17 +...
Click here to see answer by checkley71(8403)

Question 30511: What is the arithmetic mean of the numbers 5 and 3125?
Click here to see answer by checkley71(8403)

Question 30509: What is the geometric mean of the numbers 5 and 3125?
Click here to see answer by sdmmadam@yahoo.com(530)

Question 30512: If we played the Tower of Hanoi game with 20 rings, how many moves would be required?
A. 1023
B. 2046
C. 1048575
D. 2097150
Click here to see answer by Earlsdon(6294)

Question 30128: THE COST FOR PAINT TO COVER BOTH SIDES OF A LARGE ROAD-SIDE SIGN (FRONT SIDE AND BACK SIDE) WAS $150. A 5-GALLON CAN OF PAINT COSTS $25 AND WILL COVER 250 SQUARE FEET. THE SIGN IS CONSTRUCTED IN THE SHAPE OF A TRAPEZOID. IT HAS ONE BASE MEASURING 35 FT AND ONE BASE MEASURING 40 FT. WHAT IS THE ALTITUDE OF THIS TRAPEZOID?
Click here to see answer by checkley71(8403)

Question 30652: A two-digit number is six times the sum of its digits. The tens digit is 1 more than the units digit. Find the number. I dont even know where to begin with this one. Thanks for the help
Click here to see answer by Paul(988)

Question 30728: How would this sequence of numbers be solved? I don't know how to type in in.Open parenthesis, two, b to the fourth power, c to the third, close parenthesis, Open parenthesis, three a to the second power, b to the negative second power. (2b(to the fourth power)c(to the third)(3a(to the second power)b(to the -2))
Click here to see answer by Cintchr(481)

Question 31235: What is the value of Summation(k from 1 to 6(sin(2*pi*k/7)+i*cos(2*pi*k/7)));
where k is a number taking the values 1 to 6;
pi is 22/7;
i is the square-root of (-1);
Click here to see answer by venugopalramana(3286)

Question 31624: Question:
Find the sum of the grometric series: 16, -4, 1, -1/4...
(A) 4415/320
(B) 4095/320
(C) 64/5
(D) 16,383/1280
Im stuck- thanks for your help!
Click here to see answer by venugopalramana(3286)

Question 31623: Question:
Find the seventh term of the arithmetic sequence if the first term is -6 and the common difference is 5.
(A) 29
(B) 24
(C) -36
(D) 34
Thank you!
Click here to see answer by venugopalramana(3286)

Question 31731: The problem is to find the general equation for the sequence, {-1,3,-5,7,-9,11,-13,15...}. I know that -1+4=3;-1-4=-5; -1+8=7;-1-8=-9; etc...so I am guessing it involves 4*n since the difference between the numbers is 4,8,12,16,20,24,28 respectively. Also, the alternating signs indicate -1^n. I also wondered if it involved absolute value. I just haven't been able to put it together with the formula for an arithmetic sequence.
Click here to see answer by venugopalramana(3286)

Question 32431: how do you find arithmetic means in the sequence _, 6, _,_,-3, _?
Click here to see answer by mukhopadhyay(490)

Question 32712: 1. Determine the 50th term of the following sequence:
165; 160; 155; ...

Click here to see answer by mukhopadhyay(490)

Question 33102: a) Determine the sum of the first 20 terms of the following sequence:
4; 8; 16; ...
b) The sum of the first four terms of an arithmetic progression that consists of 20 terms is 21. The sum of the last three terms is 90. Determine the first term and the common difference.
Click here to see answer by mukhopadhyay(490)

Question 33100: Determine the 20th term of the following sequence:
303831; 101277; 33759; ....
Click here to see answer by mukhopadhyay(490)

Question 33525: the sum of the first nine terms of an arithmetic progression is 75 and the twenty-fifth is also 75. find the common difference and the sum of the first hundred terms.
Click here to see answer by longjonsilver(2297)

Question 33627: Please help me explan the steps to any of theae problems or all as you may, it will be very helpful.I have a quiz on it on monday. Thanks for all your Help,I appreciate it with all my Heart.Thanks
Find the indicated term given two other terms
5th term:t4=7 and t7=22
For each arithmetic series,Find S-25
7+13+19+25.....
Based on the terms given,state whether or not each sequence is arithmetic, If it is, identify the common difference,d.
15,18,21,24
Click here to see answer by sarah_adam(201)

Question 33641: I need to find a formula for the nth term from the following arithmetic sequence. Then find the fiftieth term: 3,7,11,15,... Thank you for attempting to help me solve this problem.
This problem is from a made up worksheet.
Click here to see answer by Nate(3500)

Question 33818: 1)Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a)What is d, the difference between any 2 terms?
Answer:
Show work in this space.

b)Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer:
Show work in this space.

c)Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Answer:
Show work in this space

d)Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?
Answer:
Show work in this space

e)What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)?
Answer:

2)Use the geometric sequence of numbers 1, 2, 4, 8,…to find the following:
a)What is r, the ratio between 2 consecutive terms?
Answer:
Show work in this space.

b) Using the formula for the nth term of a geometric sequence, what is the 24th term?
Answer:
Show work in this space.

c)Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Answer:
Show work in this space

3)Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,…to find the following:
a)What is r, the ratio between 2 consecutive terms?
Answer:
Show work in this space.

b)Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals.
Answer:
Show work in this space.

c)Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Please round your answer to 4 decimals.
Answer:
Show work in this space.

d)What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?
Answer:

Click here to see answer by venugopalramana(3286)

Question 34385: what is the equation and answer for 11/2,25/6,17/6,3/2,1/6
Click here to see answer by checkley71(8403)

Question 34396: 4)CLASSIC PROBLEM - A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter’s life. Mr. Brown insisted on giving the man an award for his heroism.
So, the salesman said, “If you insist, I do not want much. Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the third square. Continue this until all 64 squares are covered with pennies.” As he’d been saving pennies for over 25 years, Mr. Brown did not consider this much of an award, but soon realized he made a miscalculation on the amount of money involved.
a)How much money would Mr. Brown have to put on the 32nd square?
Answer:
Show work in this space
b)How much would the traveling salesman receive if the checkerboard only had 32 squares?
Answer:
Show work in this space
c)Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How much money would the farmer need to give the salesman?
Answer:
Show work in this space

Click here to see answer by hydromojo(20)

Question 34786: I am totally lost on this. Please help!
Write the first 5 terms of the sequence a(n)=n^2+1
Thanks in advance
Click here to see answer by usyim88hk(157)

Question 35194: find the third, fourth and fifth terms.
t sub(1) = 6; t sub(n) = t sub(n-1) + 4
Click here to see answer by venugopalramana(3286)

Question 33999: A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving hsi daughter's life. Mr. Brown insisted on giving the man an award for his heroism.
So, the salesman said, "If you insist, I don not want much. Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the third square. Continue this until all 64 squares are covered with pennies." As he'd been saving pennies for over 25 years, Mr Brown did not consider this much of an award, but soon realized he mad a miscalculation on the amount of money involved.
a)How much money would Mr. Brown have to put on the 32nd square? Show work
b)How much would the traveling salesman receive if the checkerboard only had 32 squares?show work
C) Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How much money would the farmer need to give the salesman? Show work.
Click here to see answer by venugopalramana(3286)

Question 35496: determine the sum for the geometric sequence:
n=12 , r=3 , T1 = 1/9
Click here to see answer by venugopalramana(3286)

Question 35496: determine the sum for the geometric sequence:
n=12 , r=3 , T1 = 1/9
Click here to see answer by Prithwis(166)

Question 35602: I dont even know where to start the question is
Find the common difference of the arithmetic sequence:
1/2, 1/6, -1/6, -1/2
Click here to see answer by rapaljer(4667)

Question 35638: I think this is the right category to put this in
Evaluate the factorial expression.
(n+5)!/n+5
I got n+5! as my answer. is that right?
Click here to see answer by rapaljer(4667)

Question 35713: 40,-20,10,-5,...:t8
Click here to see answer by AnlytcPhil(1278)

Question 35878: a. find the sum of the first n terms of the arithmetic series.
b. find n for the given sum S sub n.
45. 3+8+13+18+23+...
a. n=20 b. S sub n=366
Click here to see answer by venugopalramana(3286)

Question 35890: Let a1, a2, a3,.......an,....be an arithmetic sequence. Find the indicated quatitties. Could someone please help me with this? a1=-11,d=4;a2=?,a3=?a4=?
Thank you!
Click here to see answer by longjonsilver(2297)

Question 35889: Write the fiftieth term of the sequence "a" with an "n" under it=n^2+1 HELP! Thank you.
Click here to see answer by venugopalramana(3286)

Question 36032: The book is very vague about this. Find the common difference of the sequence in which the first term is 5 and the 11th term is -10. Any help appreciated.
jp
Click here to see answer by venugopalramana(3286)

Question 36110: Write the first five terms of the follownig sequence.
a sub n = n + 1/ n with the condition: a sub n= a sub n-1 + 2, where a sub n= 1
Click here to see answer by venugopalramana(3286)

Question 36558:
4) CLASSIC PROBLEM - A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter’s life. Mr. Brown insisted on giving the man an award for his heroism.
So, the salesman said, “If you insist, I do not want much. Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the third square. Continue this until all 64 squares are covered with pennies.” As he’d been saving pennies for over 25 years, Mr. Brown did not consider this much of an award, but soon realized he made a miscalculation on the amount of money involved.
a) How much money would Mr. Brown have to put on the 32nd square?
Answer:
Show work in this space

b) How much would the traveling salesman receive if the checkerboard only had 32 squares?
Answer:
Show work in this space

c) Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How much money would the farmer need to give the salesman?
Answer:
Click here to see answer by venugopalramana(3286)

Question 36552: The sum of a geometric series is 57232. The common ratio is 2 and the last term is 28672. What is the first term?
Click here to see answer by venugopalramana(3286)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690